Nonparametric Spatial Modeling towards the Mode

Existing models for spatial data analysis typically rely on mean or quantile regression to model the association between a dependent variable and covariates.We in this paper propose a novel spatial modal regression by assuming that the conditional mode of the response Y given covariates X follows a nonparametric regression structure, defined as m :and i Z N .The suggested spatial modal regression can be utilized to capture the "most likely" effect and may reveal new interesting data structures that are possibly missed by the conditional mean or quantiles, especially in cases of asymmetric data distributions.We derive the asymptotic distributions for the resulting modal estimators with appropriate choices of bandwidths.To numerically estimate the developed model, we recommend a modified modal expectation-maximization (MEM) algorithm with the assistance of a Gaussian kernel.Numerical examples are presented to demonstrate the favorable finite sample performance of the estimators.We also generalize the propounded spatial modal regression to an additive sum form to offer a versatile solution to handle high-dimensional datasets.